Can a polynomial have local extrema without having any real zeros?

Science & Mathematics by Anonymous 2018-07-11 20:33:58

Social Science

5 answers

Anonymous

Yes for example f(x) = x^2 + 5
Anonymous

y = x² + 1 Parabola that does not cross the x-axis.
Anonymous

y(x)=x^4-4x^2+8 You can have both local maximum (just one) and two local minima. See: http://www.wolframalpha.com/input/?i=y(x...
Anonymous

FALSE
Anonymous

How about f(x) = 1 + x^2 Local minimum at x=0, but no real zeroes